## Abstract

Approaching the atomic nucleus at low excitation energy (excitation energy less than the nucleon separation energy) can be done on a non-relativistic level. If we start from an
where , with , and . It is a task to determine

*A*-nucleon problem interacting via a given two-body potential*V*_{i, j}, the non-relativistic Hamiltonian can be written as$$H = \sum\limits_{i = 1}^A {t_2 + \frac{1}{2}\sum\limits_{i,j = 1}^A {V_{i,j} } } ,$$

*t*_{i}is the kinetic energy of the nucleon motion. Much experimental evidence for an average, single-particle independent motion of nucleons exists, a point of view that is not immediately obvious from the above Hamiltonian. This idea acts as a guide making a separation of the Hamiltonian into*A*one-body Hamiltonians (described by an average one-body potential*U*_{i}) and residual interactions. This can be formally done by writing$$H = {{H}_{0}} + {{H}_{{res}}}$$

$${{H}_{0}} = \sum\limits_{{i = 1}}^{A} {\left\{ {{{t}_{i}} + {{U}_{i}}} \right\}}$$

$${{H}_{{res}}} = \tfrac{1}{2}\sum\limits_{{i,j = 1}}^{A} {{{V}_{{i,j}}}} - \sum\limits_{{i = 1}}^{A} {{{U}_{i}}}$$

*U*_{i}as well as possible such that the residual interaction*H*_{res}remains as a small perturbation on the independent*A*-nucleon system. This task can be accomplished by modern Hartree-Fock methods where the residual interaction with which one starts is somewhat more complicated such as the Skyrme-type interactions (two-body plus three-body terms) which have been used with considerable success. This process of going from the two-body interaction*V*_{i, j}towards a one-body potential is drawn schematically.### Keywords

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1994